Is this the one? We may have
found the cell that will revolutionise medicine

IT MIGHT turn out to be the most important cell ever discovered.
It's a stem cell found in adults that can turn into every single
tissue in the body.

Until now, only stem cells from early embryos were thought
to be able to do this. If the finding is confirmed, it will mean
cells from your own body could one day be turned into all sorts
of perfectly matched replacement tissues and even organs.

If so, there would be no need to resort to therapeutic cloning-cloning
people to get matching stem cells from the resulting embryos.
Nor would you have to genetically engineer embryonic stem cells
(ESCS) to create a "one cell fits all" line that doesn't
trigger immune rejection. The discovery of such versatile adult
stem cells will also fan the debate about whether embryonic stem
cell research is justified.

"The work is very exciting," says Ihor Lemischka
of Princeton University. "They can differentiate into pretty
much everything that an embryonic stem cell can differentiate
into." The cells were found in the bone marrow of adults
by Catherine Verfaillie at the University of Minnesota. Extraordinary
claims require extraordinary proof, and though the team has so
far published little, a patent application seen by New Scientist
shows the team has carried out extensive experiments. These confirm
that the cells - dubbed multipotent adult progenitor cells, or
MAPCs-have the same potential as ESCs. "It's very dramatic,
the kinds of observations [Verfaillie] is reporting,' says Irving
Weissman of Stanford University. 'The findings, if reproducible,
are remarkable." At least two other labs claim to have found
similar cells in mice, and one biotech company, MorphoGen Pharmaceuticals
of San Diego, says it has found them in skin and muscle as well
as human bone marrow. But Verfaillie's team appears to be the
first to carry out the key experiments needed to back up the claim
that these adult stem cells are as versatile as ESCS.

Verfaillie extracted the MAPCs from the bone marrow of mice,
rats and humans in a series of stages. Cells that don't carry
certain surface markers, or don't grow under certain conditions,
are gradually eliminated, leaving a population rich in MAPCs.
Verfaillie says her lab has reliably isolated the cells from about
70 per cent of the 100 or so human volunteers who donated maerrow
samples.

The cells seem to grow indefinitely in culture, like ESCS.
Some cell lines have been growing for almost two years and have
kept their characteristics, with no signs of ageing, she says.
Given the right conditions,

MAPCs can turn into a myriad of tissue types: muscle, cartilage,
bone, liver and different types of neurons and brain cells. Crucially,
using a technique called retroviral marking, Verfaillie has show,n
that the descendants of a single cell can turn into all these
different cell types-a key experiment in proving that MAPCs are
truly versatile.

Also, Verfaillie's group has done the tests that are perhaps
the gold standard in assessing a cell's plasticity. She placed
single MAPCs from humans and mice into very early mouse embryos,
when they are just a ball of cells. Analyses of mice born after
the experiment reveal that a single MAPC can contribute to all
the body's tissues.

MAPCs have many of the properties of ESCs, but they are not
identical. Unlike ESCs, for example, they do not seem to form
cancerous masses if you inject them into adults. This would obviously
be highly desirable if confirmed.

"The data looks very good, it's very hard to find any
flaws," says Lemischka. But it still has to be independently
confirmed by other groups, he adds.

Meanwhile, there are some fundamental questions that must be
answered, experts say. One is whether MAPCS really form functioning
cells. Stem cells that differentiate may express markers characteristic
of many different cell types, says Freda Miller of McGill University.
But simply detecting markers for, say, neural tissue doesn't prove
that a stem cell really has become a working neuron.

Verfaillie's findings also raise questions about the nature
of stem cells. Her team thinks that MAPCs are rare cells present
in the bone marrow that can be fished out through a series of
enriching steps. But others think the selection process actually
creates th@ MAPCS. "I don't think there is la cell' that
is lurking there that can do this. I think that Catherine has
found a way to produce a cell that can behave this way,"
says Neil Theise of New York University Medical School. Sylvia
Pag6n Westphat, Boston

Alchemy for beginners To turn base metals into gold,
first boil your nuclei

THE atomic nucleus behaves so much like a drop of liquid, it
can actually boil, say physicists who have measured the properties
of nuclear "vapour" for the first time. Their discovery
is helping to explain how heavy elements such as gold, lead and
uranium are made inside supernovae.

Strong nuclear forces hold protons and neutrons together in
nuclei in much the same way that electromagnetic forces bind the
molecules in a droplet of water. In nuclear reactions the minuscule
"droplet" can spin, bulge or split, but until now no
one had found a way to discover whether it can boil. "You
can't stick a thermometer in the nucleus," James Elliott
at Lawrence Berkeley National Laboratory in California points
out. Now Vic Viola of Indiana University in Bloomington and his
colleagues have cracked the problem. At Brookhaven National Laboratory
in New York, they accelerated particles called pions to 99.9 per
cent of the speed of light and smashed them into gold nuclei.
By looking at the size of the nuclear blobs that were thrown out,
they were able to measure the nuclei's transition from liquid
to vapour.

As the energy of the pions increased, so did the size of the
blobs. But eventually they stopped getting bigger-showing that
the additional energy was being used to change the state of the
nuclei from liquid to gas. And when the researchers cranked up
the energy even further, the chunks suddenly got smallel This
indicates that all the nuclei have been vaporised, says Viola.
'If you vaporise a drop of water and look at the gas coming off,
you see small clusters of just two or three molecules," he
says.

When researchers at Lawrence Berkeley and Michigan State University
used Viola's data to calculate the boiling points of different
nuclei, they found they are typically billions of times greater
than those of atoms, around 100 billion degrees kelvin. And when
they measured the density of the nuclear vapour, its pressure
was proportional to its temperature, just as in an ordinary gas.

This new understanding of nuclear matter is already helping
other researchers to model supernovae-exploding stars that generate
heavy elements such as gold from nuclei no heavier than iron.
No one fully understands how the nuclei capture the extra neutrons
to form heavy elements, but Chikako Ishizuka and colleagues at
Hokkaido University in Sapporo, Japan, say that when nuclei boil,
it's easier for them to incorporate extra neutrons. Then they
can condense into heavy elements as they cool.

Viola says knowing how nuclei change from one state to another
is crucial to understanding a range of processes. "Now we
can describe nuclear physics under any conditions," he says.
Eugenie Samuel More at: Physical Review Letters (vol 88, p 022701)

Keep young and beautiful
Believe it or not there's already a drug that slows ageing

IT SEEMS like the ultimate elixir-a drug that extends your
lifespan while maintaining your youthful health and vigour. What's
more, in the US it's already approved for human use. There is
just one snag: to reap the benefits, you have to be a fruit fly.
Even so, the discovery promises to open up new leads in the quest
to understand longevity and ageing, says Tom Kirkwood, an expert
on ageing at the University of Newcastle upon @ne. 'What we are
looking at here is a pretty fundamental mechanism."

This is the first time that simply feeding a drug to flies
has made them live longer. And in a twist that contradicts theories
on ageing, there seems to be no price to pay for this extra time.
The flies are as healthy and fecund as their untreated peers.

Kyung-Tai Min and a team of researchers at the National Institutes
of Health and the California Institute of Technology made the
discovery by accident when they were testing a drug called 4-phenylbutyrate
(PBA) on flies with neurodegenerative disease. They found that
feeding the drug extended maximum lifespan of healthy flies by
over 50 per cent, and their average lifespan by one-third. Intriguingly,
higher doses of the drug were either toxic or less effective,
hinting that you need to strike a delicate balance to maximise
the repair mechanisms in cells.

Previous studies suggest that reduced fertility and semi-starvation
can extend fruit flies' lifespan, so the team wondered whether
PBA was mimicking these effects. But when they weighed the flies
and counted their offspring, they found they were normal.

To test the flies' resistance to stress, they then starved
them and fed them a chemical that generates free radicals. But
far from having to pay for their longevity with a weaker constitution,
the PBA flies survived better than the controls. 'We are going
to test more, but so far, it seems they are perfect,' says Min.

Kirkwood, however, is sceptical. "The drug might be incur
ring a cost that isn't visible yet,' he says. For instance, the
pampered lab flies may have to eat more than usual to keep them
going. 'They might not be so competitive in the wild."

PBA works its dramatic effects by blocking the activity of
histone deacetylases, enzymes involved in switching genes on and
off. Min found that 100 genes were switched on in response to
PBA, including the one for superoxide dismutase, a protein well
known for its anti ageing effects. About 50 others were switched
off. Minis team are investigating these genes, and how PBA has
its effect on the histone deacetylases.

So will we be popping anti-ageing pills any time soon? Kirk
wood thinks not. "It's just not that easy to bring about
changes which alter lifespan without deleterious effects,' he
says.

Unlike flies, mammalian cells continue to divide and renew
throughout life, so inducing large changes in gene expression
may be risky. However, Min points out that PBA has been approved
in the US for treating cystic fibrosis and sickle cell anaemia,
and seems to have few side effects. He and his team will be testing
the drug on mice very soon. Claire Ainsworth

More at: Proceedings of the Notional Academy of Sciences (vol
99, p 838)

Destroyer of worlds They bring death and destruction-and
a fortune in gold

AN ASTEROID that wiped out huge swathes of life when it collided
with Earth 360 million years ago may also have brought with it
untapped mineral wealth.

Robert lasky of Western Australia's Department of Mineral and
Petroleum Resources (DMPR) discovered the 120-kilometre wide Woodleigh
impact crater accidentally as he was drilling for coal near Shark
Bay, 650 kilometres north of Perth. When lasky and his colleagues
drilled down into the crater, which is buried under up to 600
metres of rock and sand, they discovered a huge chunk of dense
granite that had been dragged upwards as the ground rebounded
when the asteroid hit.

Mineralogist Franco Pirajno of the DMPR has now analysed samples
of the granite and was surprised to find that it contains valuable
elements such as magnesium, copper, chromium and nickel, which
is unusual in this kind of rock.

Instead of the asteroid being vaporised and spread through
the air over a wide area, Pirajno concludes that many of its eompo-

nents must have been incorporated into the surrounding hot
granite. The rock would have been crushed undeftpressures of around
100,000 atmospheres. "It must have created one hell of a
bang," he says. Gold deposits may also have formed as streams
of hot water ran through cracks in the rock.

But although the asteroid may have left behind a valuable legacy
for mining companies, its impact at the time would have been devastating.
Dating of the rock samples has revealed that the collision happened
360 million years ago-the time of a mass extinction towards the
end of the Devonian period, when 85 per cent of all species were
wiped out. Geologists have long speculated that an asteroid may
have been responsible, but until now there was no known impact
that could have triggered the catastrophe.

The Woodleigh asteroid certainly had enough destructive potential-it
was about five kilometres wide, making it the fourth largest asteroid
collision ever discovered on Earth, almost as big as the Mexican
Chicxulub collision that's thought to have wiped out the dinosaurs
65 million years ago. The impact would have been felt globally,
triggering earthquakes and volcanic activity, as well as creating
a cloud of dust that spread around the world, blocking out sunlight.

Lasky believes more craters may lie hidden under Western Australia's
red deserts and is keen to keep searching. But Pirajno says it
is now up to the mining companies to investigate the economic
potential of the Woodleigh site. Peter Hadfield, Sydney

Stay of execution Why one of the world's deadliest killers
has won another reprieve

SMALLPOX is one of the biggest killers in history. But now
we have it at our mercy, with the virus apparently surviving in
only two labs, in the US and Russia. So why, instead of delivering
the promised coup de grAce, did the World Health Organization
last week vote to postpone its destruction?

The WHO says it is to allow research to continue. But as recently
as last October, D. A. Henderson, who led the smallpox eradication
campaign, argued that the last official stocks of virus should
be destroyed. The live virus is useless for testing potential
new drugs or vaccines, he wrote, as it only infects people, and
people no longer get smallpox.

So what's changed? The answer, New Scientist has learned, is
that Peter Jahrling's team at the US Army Medical Research Institute
for Infectious Diseases at Fort Detrick, Maryland, has finally
managed to infect a handful of cynomolgus macaques with smallpox.
They do not yet have a perfect animal model for the disease. But
the researchers hope they will soon be able to test new vaccines,
drugs and diagnostic tools for smallpox.

Such progress helped the US persuade the WHO's executive council
to vote to postpone destruction. Not that the US would have destroyed
its stock even if the vote had gone the other way. This November,
after the 11 September attacks and the anthrax scares, US Secretary
of Health Tommy Thompson announced that the US would hang on to
its stocks "until adequate medical tools are available to
counter any future outbreak of this disease". Of course,
if the official stocks really were all that's left of the virus,
there would be no need for any defences once they were destroyed.
After smallpox was officially eradicated in 1980, the WHO asked
all countries to destroy their samples or send them to the official
repositories in the US and Russia. It then planned to destroy
these stocks. But in 1999, the US convinced WHO members to put
off destruction until 2002, amid rising fears that other, clandestine
stocks might be used as weapons, meaning live virus was needed
for defensive research. "The evidence that anyone else has
the virus is circumstantial," says Jonathan Tucker of the
Monterey Institute of International Studies. Nevertheless, it
is "highly likely", says Alan Zelicoff of Sandia National
Laboratories in New Mexico. "It is not credible that all
nations would give up their stocks at a UN request," he says.
Antibodies in soldiers defecting ftom North Korea reveal recent
vaccination against smallpox-probably, says Zelicoff, because
North Korea has a smallpox weapon. Iraq is also implicated. And
not all of the 100 tonnes of virus the Soviets weaponised per
year in the 1980s may have been destroyed. While the existing
vaccine is effective, says David Heymann, head of infectious diseases
at the WHO, it is a live virus related to smallpox with rare but
potentially fatal side effects. And it can make people with impaired
immunity seriously ill. But you can only truly test a replacement
for it against real smallpox virus. Enter the macaques. But there
are problems. So far the animals only get sick after very large
doses of virus, which makes testing vaccines difficult as enough
bugs can defeat any vaccine. And health officials are looking
for a drug that works after symptoms start-unlike cidofovir, the
only known anti-smallpox drug. But most infected macaques die
before developing full-blown symptoms like those in humans, making
tests difficult. The system merely needs development, says Heymann.
Whatever the fortunes of the team at USAMRIID, political pressures
in the US are likely to ensure that this research will continue.
Ironically, it will only be a success if it is never used. Debora
MacKenzie

Daddy's girls A hint of your
father tums a perfect stranger into an ideal mate

WOMEN seem to be drawn to men who smell like their father.
In a test that involved women sniffing unwashed T-shirts, they
appeared to unwittingly prefer the odour of men who have genes
similar to their dad's.

This is no Freudian Oedipal complex. Instead, it appears to
be a tactic in a poorly understood evolutionary game, where the
prize is either greater resistance to disease among offspring,
or an unconscious ability to spot distant relatives in a sea of
strangers.

The genes in question form part of the major histocori3patibility
complex, or MHC, which encode parts of the immune system. These
genes are thought to be closely linked to others th,* dictate
our natural odour.

These findings come as a surprise, because female mice are
known to sniff out males with MHCs different from their own, preferring
them to mates with a similar genetic make-up. And women were thought
to do the same, according to a study in which women sniffed T-shirts
that had been worn by men (New Scientist, 6 May 1995, p 19). But
the new study paints a more complicated picture. Martha McClintock,
Carole Ober and a team at the University of Chicago studied 49
women whose own and whose parents' MHC genes were known. The women
sniffed T-shirts unrelated men had worn, as in the earlier study,
but this time they had no idea what they were smelling. They were
asked to say which odours they would prefer if they had to smell
them all the time.

Surprisingly, the women preferred the odours of men who had
some MHC genes, or alleles, in common with them. On average, the
owner of a woman's most preferred odour shared 1.4 alleles with
her, whereas the owner with the least appealing odour shared 0.6.
What's more, the alleles that matched were those that the women
had inherited from their fathers.

That goes against the prevailing theory that outbreeding-seeking
mates who are genetically dissimilar to you-is always best. Going
for a mate with different immune system genes from your own should
ensure that your children have the biggest possible arsenal for
attacking pathogens. Also, the rarer their MHC, the less likely
it is that pathogens will have evolved to outsmart them.

But McClintock thinks that interpretation is too narrow. Limited
inbreeding can work, as it may actually make sense to stick with
combinations of genes that are proven to successfully fight disease.
'There's an intermediate number of matches that's probably optimal,'
she says.

Wayne Potts of the University of Utah in Salt Lake City has
a different explanation.

Although mice go for mates with different MHC genes, they prefer
to share a nest with mice with a similar MHC genetic make-up,
probably to ensure they are near their kin. Woman may be attracted
to their father's odour for a similar reason-so they can home
in-on relatives.

Potts says that Ober's own studies show women tend to marry
MHC-dissimilar men (New Scientist, 10 February 2001, p 36). And
marriage may be a more reliable indicator than old T-shirts, he
points out. Alison Motiuk More at: Nature Genetics (DOI: 101038/ng8301

Bridge the world Now's your
chance to find out how well connected you are

IF YOU get unexpected e-mail from an American university over
the coming months, don't just assume it's junk. It could be from
scientists investigating a fascinating social phenomenon.

According to urban folklore, everyone in the world knows everyone
else via just a few intermediaries-an effect summed up by the
phrase 'six degrees of separation". The number six emerged
from an experiment performed in 1967 by the social psychologist
Stanley Milgram, who sent packages to several hundred randomly
selected people in America's Midwest, with the aim of getting
them delivered to target people in Boston.

Each recipient was given some details about the target, such
as their name and profession, and was asked to send the package
to a personal acquaintance whom they believed was more likely
to know the target personally.

Milgram discovered that on average the packages reached their
targets after passing through astonishingly short chains, typically
comprising just six people. In 1998, mathematicians Duncan Watts
and Steven Strogatz at Cornell University showed that Milgram's
finding can be explained by the 'small world effect", in
which just a handful of people with very diverse friends can "short
circuit" otherwise huge networks of acquaintances (New Scientist,
6 June 1998, p 7).

But attempts to replicate Milgram's findings have had mixed
results-and in any case, the original experiment fell far short
of proving that the "six degrees" effect holds true
for the whole world. So a team at Columbia University is now using
the Internet to attempt a global version.

Instead of a postal package, they are inviting people to use
their network of acquaintances to get an e-mail message to targets
spread across the world. According to Watts, who devised the experiment,
e-mail is ideal for testing Milgram's claim as there are well
over 100 million e-mail users worldwide. Only e-mails between
genuine acquaintances will be deemed to complete a chain. People
won't be allowed to short-circuit the sequence by just looking
up the target's e-mail address.

Watts has set up a website giving full details about how to
take part, and how to volunteer to act as a target. 'Ideally,
we'd like to have, say, 100,000 people, each trying to reach around
20 targets," he says.

The team is keen to have as many people take part as possible,
not least because they suspect people's mistrust of unsolicited
e-mail might otherwise scupper their experiment. Early tests show
that barely I in 4 e-mails are being passed on. With such a high
rate of attrition, many thousands of people would have to take
part to give much chance of even one chain of acquaintances reaching
the target if Milgram's six degrees apply worldwide.

"Perhaps people can't be bothered to pass them on-or perhaps
Milgram was just wrong," says Watts. "Either way, we
need lots of people to take part so we can tell." Robert
Matthews More at: hftp://smallwor[d.sociologycolumbia.edu/index.htm[

Men of God IT'S time to recant
the orthodoxy that women are the more pious sex.

A new multi-faith StUdy of religious behaviour In Britain reveals
that men are more likely than women to practise their religion-in
every major faith bar Christianity.

That doesn't mean that women';s religious feelings or experiences
ave weaker than men's, cautions psychologist Kate Loewervthal.
The difference may reflect cultural influences. For instance,
Muslims and Jews generally consider the religious role of men
more important, and women are under less pressure to attend places
of warship. In some cases they are actively discouraged-women
are not supposed to enter a mosque ff they are menstrtating, for
example. The traditional view that women are the more pious sex
Is based on studies done almost exclusively on Christians, says
Loewenthal. So her teem at Royal Holloway University of London
studied 530 Christian, Hindu, Jewish and Muslim men and women
about their religious pracuceThe team assessed activity such as
prayer, study of religious texts and visits to a place of worship.
"We found that in the non-Christian religions in Britain
the men were more religious than the women,' says Loewenthal Daniel
Batson, a prychologist at the University of Kansas, agrees that
the findings could be due to cultural differences among the religions.
But he cautions that British culture could also be having some
unforeseen effect. "Europe is quite different in religion
from the US," he says. "in Europe, religion is not seen
as the bastion of culture that it once was." Betsy Mason
More at: Personality and individual Differences (vol 32, p 133)

Power surge Renewable energy's latest contender is lurking
by a coast near you

A TIDAL power station that taps the surging power of strong
underwater currents will be tested for the first time this summer.
In Britain, there are about 40 key locations around the coastlines
where, in theory, there's enough energy in tidal streams to generate
up to a quarter of the nation's electricity.

Wind creates waves on the sea surface, but as wind blows intermittently,
wave power is quite unpredictable. But tides are regular, as they
are caused by the gravitational pull of the Moon and Sun on large
masses of water. If the local geography is right, ocean channels
create fast-moving "tidal streams", where vast masses
of rising or falling water are squeezed into a restricted space.
But no one has proved that extracting energy from tidal streams
is practical.

That could soon change. The British government is now looking
for new energy sources to help cut carbon emissions. And this
month, British offshore equipment company Engineering Business
was given a fl.l million government grant to build a 1 SO-kilowatt
prototype tidal power station. Dubbed Stingray, the machine should
be installed between May and September on the seabed to the south-east
of the Sound of Yell, off mainland Shetland. A pair of 15-metre-long
hydroplanes, mounted on a stand, will oscillate with the tide
to drive a hydraulic motor that generates electricity (see animation
on the Web at www.engb. com/Pages/animation.htm).

Hydraulic pistons control the angle at which Stingray's hydroplanes
face the tidal current to make the most of the onrushing water.
Like an aircraft wing, their angle of attack-the angle at which
it bites into the current-changes to create "lift",
which pulls the hydroplane up and down. As they move, the hydroplanes
yank on an attached arm that pumps high-pressure oil through a
hydraulic motor, which turns an electric generator.

Although the design is still being finalised, the structure
is expected to weigh 35 tonnes, rise to 20 metres above the seabed
and work in currents of between 2 and 3 metres per second (4 to
6 knots). Most of it will be made of steel, though the hydroplanes
could be cast in glassreinforced plastic.

Stingray may only work with the tide flowing in one direction,
but its successors will swivel round or flip over four times a
day so they can catch the tidal stream in both directions. Depending
on the site, this should mean they generate power at least three-quarters
of the time.

Engineering Business's managing director Tony Trapp told New
Scientist he is "quietly confident" that Stingray will
work, but stresses that its economics are less certain. He estimates
that it will-generate electricity for between 4.7 and 12 pence
per kilowatt-hour. Although this is more expensive than wind and
nuclear power, it is comparable to wave power-and much more predictable.

Another contender in the tidal-stream game is an underwater
windmill developed by Marine Current Turbines of London. A prototype
that generates power using the circular motion of propeller-like
turbines was originally due for installation off the coast of
south-west England in 2000 (New Scientist, 20june 1998, p 38).
But according to MCT's Peter Fraenkel, it was postponed because
of delays in getting almost El million in government funding.
Now he has the money, Fraenkel is planning to install a 300-kilowatt
underwater windmill north-east of Lynmouth, Devon, in September.
But both Fraenkel and Trapp insist they are not racing to be the
first to generate tidal power. It is likely to be a multibillionpound
industry, predicts Fraenkel. "There's room for both of us."
Rob Edwards, Edinburgh

The Other Side of Zero

The opposite of infinity is a number so small that mathematicians
almost missed it entirely. Good Job they didn't, says Ian Stewart

IT IS a number like no other. It is smaller than anything except
zero, but it's not zero. It makes no logical sense, but it has
endless uses. It's the infinitesimal, and it's back. Infinitesimally
speaking, a circle is actually a polygon with infinitely many
infinitesimal sides. A solid is in fact an infinite sandwich of
infinitesimally thin slices. And velocity is an infinitesimal
distance divided by an infinitesimal time. The whole world is
made of these next-to-nothings.

Yet 19th-century purists found these tiny slices of nothing
just too much to swallow, and they were banished from mathematics
for more than a century. Only recently has the concept been restored
to respectability, and it's back with a vengeance. Infinitesimals
are now giving us insights in physics and simplifying our understanding
of key areas of pure mathematics. But how on earth can such a
peculiar notion make sense?

The idea of infinitesimals is an ancient one. Archimedes used
them to calculate the volume of a sphere. He imagined cutting
the sphere into infinitely many slices and hanging them on one
arm of a balance. He rearranged them so that they exactly balanced
a cone hanging on the other arm. Knowing how levers work, he related
the volume of the sphere to that of the cone, and out popped his
formula. It's a bizarre idea: if the slices are infinitely thin,
how can they have any weight or volume? How can you add up a lot
of zeros to get something substantial? Yet somehow it works.

The real arguments began after Newton devised his calculus,
a way to calculate rates of change, such as velocities. He looked
at the changing quantity (position, say) at two times separated
by a very short interval, and calculated a formula for the average
rate of change in that interval. Then to get the answer for a
precise moment in time, rather than the average over a short interval,
he shrank the interval in the formula to zero. That is, he did
the calculation assuming it was non-zero, and then set it to zero.
This vanishing quantity he called a 'fluxion" and, like Archimedes's
slices, it worked,

But again the logic seems faulty. Over an interval of zero
seconds, the position changes by zero, so the calculation becomes
0/0, and every mathematician knows that 0/0 can be anything you
like.

This was too much for the bishop and philosopher George Berkeley,
who in 1734 published a pamphlet called The Analyst, or a Discourse
Addressed to an Infidel Mathematician ... (the title went on a
bit). He sarcastically called Newton's fluxions "ghosts of
departed quantities". His criticisms were spot on, but people
kept on using calculus because it always gave sensible answers.
It was more like magic than mathematics, but the spell worked.

Still, mathematicians in the 19th century were troubled. If
a positive number is not zero yet is still smaller than any positive
non-zero number, then it must be smaller than itself. That's impossible.
So they found alternative ways to set up calculus, and called
the resulting formalism "analysis" to emphasise its
technically demanding foundations. Many people, especially school
teachers and students of calculus, looked wistfully over their
shoulders, because infinitesimals are much easier to handle than
the rigours of analysis. But mathematicians were determined: infinitesimals
could not possibly exist. That's because the basic ingredient
of analysis is the concept of a "real" number. And in
the technical mathematical sense of the word real, a real number
is one that can be written as a decimal. Real numbers include
all whole numbers and all fractions, together with more subtle
numbers like 'A and 42. Crucially, no matter how small a real
number is, there is always another number smaller than it-just
divide 1 by some large enough number n. This property of reals
is called the Archimedean axiom, and it leaves infinitesimals
out in the cold, since it's impossible to imagine a real number
that is like I divided by infinity. It would be a decimal with
infinitely many zeros-in other words, zero itself. It was more
than a century later, in the 1960s, before the logician Abraham
Robinson came along and spotted a way round this argument. Why
not simply accept that infinitesimals aren't, in the technical
sense, real? At least six times in the history of mathematics,
the meaning of the word number has been changed to accommodate
new variants. Even fractions and negative numbers were once considered
preposterous, but they proved indispensable and after a while
no one batted an eyelid. Mathematicians could likewise accept
and use infinitesimals, Robinson reasoned. There's no need to
pretend that they are real numbers. So Robinson abandoned the
Archimedean axiom and simply asked, what happens if we accept
that there are numbers too small to be expressed as decimals?
He worked out the arithmetic of such infinitesimals-how to do
maths with them-and found that unlike Newton's paradoxical fluxions,
they make perfect sense. You can add, subtract, multiply and divide
infinitesimals, and even combine them with real numbers to produce
"nonstandard" numbers. Adding an infinitesimal to a
real number gives you a finite nonstandard number-"three
and a vanishingly small bit", for example. Dividing a real
number such as 1 by an infinitesimal produces infinity, as you
might expect, but it is a specific infinity that makes perfect
logical sense. What's more, an infinitesimal avoids the contradiction
of having to be smaller than itself. lt only has to be smaller
than all nonzero real numbers, and that's not a problem as they
aren't real anyway. What Robinson ended up with was a new and
consistent number structure that included all the usual real numbers
and arithmetic operations, but supplemented them with the infinitesimals
and infinite numbers. This new branch of maths, known as nonstandard
analysis (NSA), cloaks each ordinary number with a cloud of nonstandard
numbers, all closer to it than any other real number and differing
from each other by an infinitesimal amount. It gives the real
numbers an infinitesimal fuzz.

Subtle knife

The upshot of Robinson's discovery is that approaches like
that of Archimedes can be made rigorous. You really can find the
volume of a sphere by adding together infinitely many infinitesimal
slices. It's as though NSA gives you a knife sharp enough to cut
it up that small and handle the pieces. This is close to our intuitive
idea of why this method works. And if the test of a mathematical
model is how easily it helps us understand the world, then infinitesimals
pass with flying colours. In a way, it seems that the world really
is made of infinitesimal pieces.

The infinitesimals and their other nonstandard companions are
now coming into their own in many areas of mathematics and physics.
Take the Boltzmann equation. This describes how a cloud of tiny
particles, such as the molecules in a gas, changes in density
as the particles move and collide. Physicists use computers to
solve the equation, to predict gas flows in interstellar clouds,
for example. The same equation can even be adapted to replace
atoms with stars, and so predict the motions of stars in a galaxy.

But the equation held a dark secret. No one had proved that
it wouldn't go haywire somewhere. That is, you couldn't be sure
that for some new situation the equation wouldn't predict points
of infinite density, or some other absurdity. And if you can't
even rely on that much, you can't trust numerical approximations
on a computer.

No one has yet found a "classical" proof that the
equation always has neat solutions, because the huge numbers of
particles that could be involved mean there are too many possible
situations to cover. But in 1984, Lars Arkeryd decided to use
infinitesimals instead. By making the molecules infinitesimally
small, he could use the mathematics of NSA to do the proof once
and for all, and he succeeded in proving that the equation is
well behaved after all. Physicists can now trust their simulations.
A case where NSA has actually given physicists new results is
Brownian motionthe apparently random movement of small bits of
dust or smoke particles caused by molecules of the surrounding
fluid buffeting them. This kind of unpredictable behaviour also
d6cribes the movement of prices in stock markets, the movement
of data in computer networks and many other situations, so if
you find a model for one you can apply it to all the related areas.
In the 1920s, Norbert Wiener of MIT discovered how to calculate
some of the characteristics of Brownian motion, by considering
the average properties of the fluid as if it were a continuous
substance-smoothing out the molecules into a continuous goo. But
Wiener's approach was extremely technical. Worse, it only revealed
the general properties of Brownian motion. There is nothing in
his theory that corresponds to the trajectory of an actual bit
of grit. It's like having a theory of the Solar System in which
there are no planets and no orbits. In 1976, Robert Anderson discovered
a much better and simpler approach to the problem using NSA. He
started by modelling the whole problem rather like a game of 3D
chess on a very large chessboard. The model chops space up into
cubes, some of which contain a piece that represents a molecule.
At each tick of a clock the pieces move randomly, either north,
south, east, west, up or down. Because this system is discrete,
the calculations can be done combinatorially-that is, by counting
things. This avoids all the technicalities of Wiener's approach,
and it's relatively easy to work out what's going on.

Of course, real molecules move continuously rather than on
a lattice. But you can easily model this with infinitesimals:
make your chessboard from infinitely many infinitesimal squares.
The successive moves are separated by a fixed, but infinitesimal,
interval of time. This way Anderson could work out real trajectories
for single dust particles, or single shares on the stock market.

Much more recently, some of the oddest aspects of infinitesimals
have been appearing in pure maths. In 2000, Viadimir Kanove of
Moscow University and Michael Reeken of Wuppertal University in
Germany published a nonstandard proof of the Jordan curve theorem.
This theorem states that every joined-up or "closed"
curve divides the plane into two distinct regions, an inside and
an outside. It may sound obvious, but it's not. Curves can be
very complicatedfor example, a spiral embellished with many smaller
spirals and so on forever. Proving the Jordan theorem for such
a curve is anything but straightforward.

It is straightforward, however, if the curve is a polygon.
To tell if a point is inside or outside, simply draw a straight
line away from the point far enough to get well away from the
polygon. If the line crosses the polygon an odd number of times
then your point is inside. If it crosses an even number of times-such
as zero-then it is outside.

Kanove and Reeken have shown that you can approximate any closed
curve by a single polygon with infinitely many infinitesimal sides.
This differs from the original curve by an infinitesimal amount,
but now you can use the same odd/even argument to prove the theorem.
The twist is that you might cross the polygon an infinite number
of times, but that's airight. With NSA you can tell if an infinite
integer is odd or even: if you can make it by multiplying some
other nonstandard infinite integer by two, then it's even. If
you have to double another infinity and then add one, it's odd.

If all that is too abstruse for you, consider something more
everyday: computer graphics. A monitor screen is composed of finitely
many tiny rectangular pixels, but it can be modelled instead as
a lattice with infinitely many infinitesimal pixels. jeanPierre
Reveill@s of Lois Pasteur University in Strasbourg has shown that
this has many advantages, especially when you want to rotate an
image through some angle.

In the ordinary case, when you rotate a finite lattice of points
through some angle, they don't usually fit very neatly into the
original grid of pixels you have on your screen, so working out
the formula for how to do it is tricky. But if you instead work
out how to do the rotation for an infinity of pixels, then you
can ifistantly adapt that formula to rotate a finite number, instead
of having to do the calculations from scratch each time. Other
manipulations can also be simplified this way, and infinitesimals
could one day be behind incredible special effects and computer
games.

And perhaps more than mere games. juha Oikkonen of the University
of Helsinki reckons that NSA will be able to answer questions
about what a computer can in principle do. "In theoretical
computer science, one studies extremely complicated finite situations,"
he says. The limits of computing power may be related to the passage
between the infinite and the finite, and Oikkonen's guess is that
infinitesimals may be the way to explore this borderline. But
for now it is only a guess.

Admittedly, infinitesimals take a little getting used to. These
slices of nothingness might seem like nonsense at first, but in
mathematics you should never give up on a good idea just because
it doesn't make sense, El